2. Describing Data with Tables and Graphs

Visualizing Qualitative vs. Quantitative Data

2. Describing Data with Tables and Graphs

Visualizing Qualitative vs. Quantitative Data

4:52 minutes

Problem 2.3.14

Textbook Question

Ideal Family Size The following USA Today–type graphic illustrates the ideal family size (total children) based on a survey of adult Americans.

a. What type of graphic is being displayed?

b. Describe any problems with the graphic.

c. Construct a graphic that is not misleading and makes the data stand out.

Verified step by step guidance

Step 1: Identify the type of graphic displayed. This graphic uses images of baby bottles to represent percentages, which is a form of pictogram or pictorial chart where the size or height of the images corresponds to the data values.

Step 2: Analyze the problems with the graphic. Notice that the baby bottles' heights are used to represent percentages, but the widths are not consistent, which can mislead the viewer because the area (height × width) might exaggerate differences. Also, the 10% 'Don't Know' category is only shown as text and not visually represented, which can cause confusion or underrepresentation of that data.

Step 3: Understand why this is misleading. In pictograms, the area of the images should be proportional to the data values, but here only the height changes while the width remains constant, or the width might also change inconsistently, leading to distorted perception of the data proportions.

Step 4: Plan a better graphic. A bar chart with uniform bar widths and heights proportional to the percentages would be clearer. Each bar should represent one category (0 to 2 children, 3 or more, and Don't Know) with heights corresponding exactly to 52%, 38%, and 10%, respectively.

Step 5: Construct the improved graphic by drawing three bars side by side, each labeled with the category and percentage. Ensure the y-axis is labeled with percentage values to provide context, and use consistent colors or patterns to differentiate categories clearly without distorting the data.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Types of Graphical Representations

Graphs visually represent data to make patterns and comparisons easier to understand. Common types include bar graphs, pie charts, and histograms. The graphic shown uses baby bottles as bars, making it a pictogram, which is a type of bar graph using images instead of plain bars.

Misleading Graphs and Visual Distortion

Graphs can be misleading if visual elements distort the data, such as using images with varying sizes that do not scale proportionally to the data values. For example, the baby bottles' heights and widths may exaggerate differences, causing misinterpretation of the actual percentages.

Effective Data Visualization Principles

Effective graphs should clearly and accurately represent data without distortion. This includes using consistent scales, avoiding unnecessary embellishments, and choosing simple formats like standard bar graphs or pie charts. Clear labeling and proportional sizing help viewers quickly grasp the data's meaning.

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Textbook Question

The U.S. Strategic Oil Reserve is a government-owned stockpile of crude oil. It was established after the oil embargo in the mid-1970s and is meant to serve as a national defense fuel reserve, as well as to offset reductions in commercial oil supplies that would threaten the U.S. economy. The graphic depicts oil reserves in 1977 and 2018.

b. The United States imported approximately 10.14 million barrels of oil per day in 2018. At that rate, assuming no change in U.S. oil production, how long would the U.S. strategic oil reserve last if no oil were imported?

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Textbook Question

Energy Need during Pregnancy The total energy need during pregnancy is normally distributed, with mean μ = 2600 kcal/day and standard deviation σ = 50 kcal/day.

Source: American Dietetic Association.

a. Is total energy need during pregnancy qualitative or quantitative?

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Textbook Question

Gas Hike The average per gallon price for regular unleaded gasoline in the United States rose from \$1.46 in 2001 to \$2.77 in 2018.

Source: U.S. Energy Information Administration

a. Construct a graphic that is not misleading to depict this situation.

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Textbook Question

Gas Hike The average per gallon price for regular unleaded gasoline in the United States rose from \$1.46 in 2001 to \$2.77 in 2018.

Source: U.S. Energy Information Administration

b. Construct a misleading graphic that makes it appear the average price roughly quadrupled between 2001 and 2018.

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Textbook Question

Retain Your Knowledge: Decision Making and Hunger Does hunger improve strategic decision making? That is, if you are hungry are you more likely to make a favorable decision when the outcome of your decision is uncertain (as in business decisions)? To test this theory, researchers randomly divided 30 normal weight individuals into two groups. All subjects were asked to refrain from eating or drinking (except water) from 11 P.M. on the day prior to their 9 A.M. meeting. At 9 A.M., the subjects were randomly assigned to one of two groups. The subjects in Group 1 were fed breakfast while the subjects in Group 2 were not fed. All subjects were administered a computerized version of an exam that assesses complex decision making under uncertain conditions. The assessment consisted of subjects choosing cards from four decks marked A, B, C, and D. Cards in decks A and B had a point value of 100 while cards in decks C and D had point values of 50. However, deck A had penalty cards that deducted points between 150 and 300; deck B had one penalty card of 1250; deck C had penalty cards between 25 and 75 points; deck D had a single penalty card of 250 points. So, decks A and B had stiffer penalties over the long haul than decks C and D and in the long haul, decks C and D resolted in more points than decks A and B. In total, the subjects would select 100 cards. However, the response variable was the number of cards selected from decks C and D out of the last 60 cards selected. The thinking here is that after 40 card selections, the subjects would be aware of the advantage of decks C and D. The researchers administered a Barret Impulsivity Scale to be sure the two groups did not differ in terms of impolsivity (e.g., “I do things without thinking”). There was no difference in impulsivity, age, or body mass index between the two groups. Before the exam, subjects were asked to report their level of hunger and it was found that Group 2 was significantly more hungry than Group 1. After analysis of the data, it was determined that the mean number of advantageous cards (decks C and D) selected by the subjects in Group 2 was 33.36 cards while the mean was 25.86 for the subjects in Group 1. The researchers concluded that hunger improves advantageous decision making.

c. What is the response variable? Is it qualitative or quantitative? If quantitative, is it discrete or continuous?

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Textbook Question

f. What are the statistics in the study?

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Textbook Question

Platelet-Rich Plasma In a prospective cohort study, 20 patients with alopecia (hair loss) had platelet-rich plasma (PRP) injected in their scalps. After three months, the mean difference in hair density (after - before) was 170.70 hairs per square centimeter with a standard deviation of 37.81hairs/cm2. Source: Gkini MA, Kouskoukis AE, Tripsianis G, Rigopoulos D, Kouskoukis K., “Study of Platelet-Rich Plasma Injections in the Treatment of Androgenetic Alopecia through a One-Year Period”. J Cutan Aesthet Surg, 2014; 7:213–219.

b. What is the variable of interest in this study? Is it qualitative or quantitative?

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Textbook Question

b. Identify the experimental units.

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